Changyu Xia

Inequalities for eigenvalues of the buckling problem of arbitrary order

This paper studies eigenvalues of the buckling problem of arbitrary order on bounded domains in Euclidean spaces and spheres. We prove universal bounds for the kth eigenvalue in terms of the lower ones independent of the domains. Our results strengthen the recent work in Jost et al. (Commun Partial Differ Equ 35:1563–1589, 2010) and generalize Cheng–Yang’s recent estimates (Cheng and Yang in Trans Am Math Soc 364:6139–6158, 2012) on the buckling eigenvalues of order two to arbitrary order.